Congrats and good luck with the first brew. I remember mine. Was nervous as hell, but 4 weeks later I couldn't have been happier. And yes, this is a cool site. I've gotten good advice and instruction from here. Let us all know how it turns out. Next time, go for the 5 gallon batch. You'll be wishing you did when its all gone too quickly.

Sure, moving it won't hurt anything. I probably wouldn't shake it, but a little agitation or swirling to try and knock down the foam (krausen) won't hurt anything.

Probably the best way to control the yeast activity and the resultant foam is to cool it down. I used to need a blow off tube now and then, but by keeping my fermentation temperatures (for ales) down around 60-64°F I usually slow everything down enough to keep the foam under control. Sometimes I'll move the beer someplace warmer as it starts to finish, just to make sure it goes to completion.

I stayed with Mr. Beer too long brewing their kits and adding stuff (DME etc.). Go for broke and get a real fermenting vessel. I personally like carboys and have used nothing less after my bout with Mr. Beer. There are plenty of good recipes posted to this site and by reviewing them you will find that there is a standard of ingredients that goes in a particular style. Above all do not get discourage when it doesn't turn out the way you planed; it's a hobby after all and enjoy the fruits of your FUN.
P.S. My Mr. Beer has been resting in the loft of my shed for a few years now. I just didn't have the heart to throw him away. I figure that I my some day find a use for him.